Question

write the coordinates of the vertices after a dilation with a scale factor of $\frac{1}{3}$, centered at the origin.

Explanation:

Step1: Identify original coordinates

From the graph, the coordinates of point \(E=(6,3)\), \(F=(6,9)\), \(G = (- 6,9)\)

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor \(k=\frac{1}{3}\), if the original point is \((x,y)\), the new point \((x',y')=(k x,k y)\).
For point \(E\):
\(x'=\frac{1}{3}\times6 = 2\), \(y'=\frac{1}{3}\times3 = 1\), so the new coordinates of \(E\) are \((2,1)\)
For point \(F\):
\(x'=\frac{1}{3}\times6 = 2\), \(y'=\frac{1}{3}\times9 = 3\), so the new coordinates of \(F\) are \((2,3)\)
For point \(G\):
\(x'=\frac{1}{3}\times(-6)=- 2\), \(y'=\frac{1}{3}\times9 = 3\), so the new coordinates of \(G\) are \((-2,3)\)

Answer:

The coordinates of \(E\) after dilation are \((2,1)\), the coordinates of \(F\) after dilation are \((2,3)\), and the coordinates of \(G\) after dilation are \((-2,3)\)